In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...

open problem on Hamiltonicity of cubic bipartite polyhedral graphs Eulerian path, a path through all edges in a graph Fleischner's theorem, on Hamiltonian...

have even degree. All Eulerian circuits are also Eulerian paths, but not all Eulerian paths are Eulerian circuits. Euler's work was presented to the St...

unicursal in Wiktionary, the free dictionary. Unicursal may refer to: Eulerian path, a sequential set of edges within a graph that reach all nodes Labyrinth...

an Eulerian path if and only if it has either 0 or 2 vertices of odd degree. If it has 0 vertices of odd degree, the Eulerian path is an Eulerian circuit...

\chi (S^{2})=F-E+V=2} Eulerian circuit, Euler cycle or Eulerian path – a path through a graph that takes each edge once Eulerian graph has all its vertices...

graph Path (graph theory) Seven Bridges of Königsberg Eulerian path Three-cottage problem Shortest path problem Dijkstra's algorithm Open Shortest Path First...

such objects. Eulerian An Eulerian path is a walk that uses every edge of a graph exactly once. An Eulerian circuit (also called an Eulerian cycle or an...

unbroken path in an order which surrounds each piece and traverses each edge only once. This process is an application of the Eulerian path. Geometry...

which is an NP-hard problem. Eulerian path strategies are computationally more tractable because they try to find a Eulerian path through a deBruijn graph...

number of edges, the resulting multigraph does not contain an Eulerian path nor an Eulerian circuit, which means that this puzzle cannot be solved. By bending...

cycles of the vertices of the five platonic solids – only the octahedron has an Eulerian path or cycle, by extending its path with the dotted one v t e...

infinite family of polyhedral graphs such that the length of the longest simple path of an n {\displaystyle n} -vertex graph in the family is O ( n α ) {\displaystyle...

constructed by taking a Hamiltonian path of an n-dimensional de Bruijn graph over k symbols (or equivalently, an Eulerian cycle of an (n − 1)-dimensional...

Euclidean traveling salesman problem Euclid's algorithm Euler cycle Eulerian graph Eulerian path exact string matching EXCELL (extendible cell) exchange sort...

MR 1241401. Pevzner, Pavel A.; Tang, Haixu; Waterman, Michael S. (2001). "An Eulerian path approach to DNA fragment assembly". Proceedings of the National Academy...

Euclid (as in Euclidean geometry, Euclidean algorithm) Eulerian – Euler (as in Eulerian path) Euripidean – Euripides Eustachian – Eustachius (as in Eustachian...

reaching the starting point (in mathematical terminology, this is a Eulerian path on a graph). Children use sticks to draw these in the dirt or sand,...

integral graph—a graph whose spectrum consists entirely of integers. An Eulerian subgraph of a graph G {\displaystyle G} is a subgraph consisting of a subset...

postman problem Vehicle routing problem Travelling salesman problem Eulerian path Capacitated arc routing problem List of graph theory problems Snow plow...

assembler. Hybrid genome assembly can also be accomplished using the Eulerian path approach. In this approach, the length of the assembled sequences does...

union or intersection of two Eulerian subgraphs may fail to be Eulerian. However, the symmetric difference of two Eulerian subgraphs (the graph consisting...

mathematics, the BEST theorem gives a product formula for the number of Eulerian circuits in directed (oriented) graphs. The name is an acronym of the names...

far. This mirrors the process of the line, which in the theory of the Eulerian path returns to the beginning. Furthermore, Kubik describes sona as being...

– euhemerism Leonhard Euler, Swiss mathematician – Euler's formula, Eulerian path, Euler equations; see also: List of topics named after Leonhard Euler...

number of Catalan paths (i.e. good paths) is obtained by removing the number of bad paths from the total number of monotonic paths of the original grid...

shortest closed path or circuit that visits every edge of an (connected) undirected graph at least once. When the graph has an Eulerian circuit (a closed...

PMC 3290790. PMID 22156294. Pevzner PA; Tang H; Waterman MS (2001). "An Eulerian path approach to DNA fragment assembly". Proceedings of the National Academy...

Édouard Lucas: Récréations Mathématiques Volume I, 1882. H. Fleischner: Eulerian Graphs and related Topics. In: Annals of Discrete Mathematics No. 50 Part...

spanning tree. Given an Eulerian graph, we can find an Eulerian tour in ⁠ O ( n ) {\displaystyle O(n)} ⁠ time, so if we had an Eulerian graph with cities from...